A391979 Number of closed "knight + wazir" tours on an 8 X n board.

0, 4, 1484, 290247, 21767466, 10808297353, 2375931620966, 460170137868876, 86120998813237562, 20912440756793175381, 4269789533989878923996, 903074393101632744082459, 186843783417066650757163898, 40434310805094436324334667019, 8440630895242498970832101406644

Offset

1,2

Comments

A "wazir" is an ancient chess piece that moves one step horizontally or vertically. A "knight + wazir" tour makes knight moves and wazir moves alternately (see example).

References

Donald E. Knuth, Hamiltonian paths and cycles, Prefascicle 8a of The Art of Computer Programming (work in progress, 2025).

Links

Don Knuth, Table of n, a(n) for n = 1..32

Example

For n=2 the a(2)=4 solutions are
   1  4     1  4     1 16     1 16
  16  5    16  5    14  3    14  3
   3  2     3  2    15  2    15  2
   6 15     6 15     4 13     4 13
   7 14     7 14     5 12     5 12
  10 11    12  9     8  9    10  7
  13  8    13  8    11  6    11  6
  12  9    10 11    10  7     8  9
(and the first and last of these have 4-way symmetry!).

Crossrefs

Cf. A193055 for knight moves only.

Sequence in context: A160088 A094546 A203035 * A030253 A278549 A229664

Adjacent sequences: A391976 A391977 A391978 * A391980 A391981 A391982

Keyword

nonn

Author

Don Knuth, Dec 25 2025

Extensions

This sequence was first computed by Peter Weigel in November 2025, and I have verified the values using a program called DYNABIDIHAM.

Status

approved